Question

In the formula $X = 3Y\, Z^{2}, X$ and $Z$ have dimensions of capacitance and magnetic induction respectively. What are the dimensions of $Y$ in $MKSQ$ system?

• A. $[ L^{ - 3} L ^{ - 1} T^3 Q^4 ]$
• B. $[ M^{ - 3} L^{ - 2} T^4 Q^4 ]$
• C. $[ M^{ - 2} L^{ - 2} T^4 q^4 ]$
• D. $[ M^{ - 3} L^{ - 2} T^4 Q]$

Answer 1

Answer: (B)

$[ M^{ - 3} L^{ - 2} T^4 Q^4 ]$

Answer 2

[ Y ] = $\bigg [ \frac{ X}{ Z^2} \bigg ] = \bigg [ \frac{ \text{Capacitance} }{ (\text{Magnetic induction} )^2 } \bigg ]$
= $\bigg [ \frac{ M^{ - 1} L^{ - 2} Q^2 T^2 }{ M^2 Q^ { - 2} T^{ - 2}} \bigg ]$
= $[ M^{ - 3} L^{ - 2} T^4 Q^4 ]$